In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control.
Quorum quenching (QQ)-based strategies are efficient for biofouling control. However, the feasibility of using QQ bacteria in antibiotic-stressed membrane bioreactors (MBRs) remains unknown. In this study, we isolated three novel QQ strains (Bacillus sp. QX01 and QX03, Delftia sp. QX14) from the activated sludge of an actual MBR. They can degrade 11 N-acyl-homoserine lactones (AHLs) with high efficiencies and rates through intracellular QQ pathways involving putative acylases and lactonases. Running two lab-scale MBRs, we found that introducing antibiotics (sulfamethoxazole, azithromycin, and ciprofloxacin, each at 100 μg/L) shortened the fouling cycle by 71.4 %. However, the immobilized inoculation of QX01 into one MBR extended the fouling cycle by 1.5-2.0 times. Quantitative detection revealed that QX01 significantly reduced the concentrations of two AHLs (C4-HSL and C8-HSL), which were positively correlated with the contents of extracellular polymeric substances (EPS) (Pearson's r = 0.62-0.83, P < 0.01). This suggests that QX01 could perform its QQ activity robustly under antibiotic stress, thereby inhibiting EPS production (proteins especially) and biofilm formation. Moreover, QX01 notably altered the succession patterns of both sludge and fouling communities, with more pronounced effects on abundant taxa. Genera associated with AHL synthesis and EPS production, such as Terrimonas and Rhodobacter, were significantly depleted, contributing to the mitigated biofouling. Additionally, QX01 increased the bacterial community diversity (evenness especially), which was inhibited by antibiotics. Overall, we demonstrate that the novel QQ bacteria could be effective for biofouling control in antibiotic-stressed MBRs, though future work is needed to develop practical approaches for prolonging QQ activity.
Wetlands are major microplastic sinks with a large atmospheric input. However, many details of such deposited atmospheric microplastics entering into wetlands remain unclear, including temporal patterns of input and ecological effects. We monitored the aerial microplastics during four seasons in eleven economically developed cities along the lower reaches of the Yangtze River Basin, China. The average microplastic deposition rate was 512.31 items m−2 d−1, equivalent to an annual contribution of 17.46 metric tons of plastic to the surveyed wetlands with a total area of 1652 km2. These microplastics were predominantly composed of polyamide and polyethylene terephthalate with 61.85 ± 92.29 µm sized pellets, and we obtained similar results for microplastics intercepted on moss in wetlands. Microplastic input varied between wet and dry periods, primarily influenced by wind, rainfall and ozone concentration. Civilian vehicle density and textile industry were the primary socioeconomic factors driving microplastic deposition. Further indoor microcosm experiments revealed that moss phyllosphere bacterial community structure and function were influenced by microplastic abundance and size, exemplifying the unique ecological risks of aerially deposited microplastics to wetlands. These results indicate that mosses and their phyllosphere microbiota could serve as bio-indicators of aerial microplastic characteristics and impacts.
As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the anti-Cheeger cut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the objective function values are monotonically updated and the iteration points converge to a local optimum in finite steps via an appropriate subgradient selection. It can also be easily combined with the maxcut iterations for breaking out of local optima and improving the solution quality thanks to the similarity between the anti-Cheeger cut problem and the maxcut problem. The performance of CIAs is fully demonstrated through numerical experiments on G-set from two aspects: one is on the solution quality where we find that the approximate solutions obtained by CIAs are of comparable quality to those by the multiple search operator heuristic method; the other is on the computational cost where we show that CIAs always run faster than the often-used continuous iterative algorithm based on the rank-two relaxation.